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Maths worksheets for challenging problem sums

Related Skills
Skill Involving Changing quantities
Ratio
Fraction

* Practice for skill involving changing quantities

1) At a 2-day seminar, each participant was charged $35 per day. On Day 1, the number of female participants was 70 fewer than the number of male participants. On Day 2, the number of male participants decreased by 20%, while the number of female participants increased by 10%. Given that there were 531 participants on Day 2, what was the total amount of money paid by all the participants on both days?

Ans :- $38535.

2) Jane and Iris had 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris. She was left with twice as many sweets as Iris.
a) How many sweets did Iris give away?
b) How many sweets did Jane have in the end?

Ans :- a) Iris gave away 60 sweets
b) In the end Jane had 120 sweets.

3) My salary is 15 more than my sister but 20% less than my brother. If our total salary is $11 100, what is my sister's salary?

Ans :- My sister's salary is $3000.

4). Alex, Brad and Clara shared some erasers in the ratio 4 : 5 : 6 at first. During a game, Brad won ¼ of Alex's erasers while Clara lost 10 erasers to Brad. As a result, Alex now has ¾ as many erasers as Clara. How many erasers did each of them have at first?

Ans :- At first Alex had 20, Brad had 25 and Clara had 30 erasers.

5) A box contains hotdog buns, custard buns and curry buns. The ratio of the number of hotdog buns to the number of custard buns is 7 : 2. The number of curry buns is 56 of the total number of hotdog and custard buns. After some hotdog buns were sold, there were an equal number of hotdog buns and custard buns. If there were 276 buns in the end, how many hotdog buns were sold?

Ans :- 120 buns were sold.

6) Valerie has 1 764 more stickers than Mark. After Mark gave Valerie 128 stickers, she had five times as many stickers as Mark. How many stickers did Mark have at first?

Ans :- At first Mark had 633 stickers.

7) Mr. Yusoff had some stationery in his shop. ¼ of them were pencils, ½ of the remainder were pens and the rest were pencil cases. The table below shows the price of the stationery.

Price of Stationery Price
1 Pencil $0.40
1 Pen $0.80
1 Pencil case $1.20

He sold some pencils, pens and pencil cases in the ratio of 3 : 4 : 5 and collected $52. Given that he sold ½ of the total number of pencils, how many pencil cases did Mr. Yusoff have at first?

Ans :- 45 pencil cases.

8) During a survey, 342 women responded that they preferred romantic comedies to other types of movies. The ratio of the number of women to the number of men who liked romantic comedies was 3 : 1.
a) How many people liked romantic comedies?
b) The ratio of the number of people who liked romantic comedies to those who did not was 2 : 3. If 25% of the people who did not like romantic comedies were women, how many men took the survey altogether?

Ans :- a) 456 people liked romantic comedies
b) 627 men took the survey altogether .

9) In a survey, some pupils were asked if they preferred volleyball or table-tennis. 1320 of the pupils chose volleyball, 75% of the pupils chose table-tennis and 5% of the pupils did not choose any of the two sports. Given that 90 pupils chose both volleyball and table-tennis, how many pupils took part in the survey?

Ans :- 200 pupils took part in survey.

10) Vanessa used some coloured beads to make a bag. 44% of the beads were red and the rest were either blue or yellow. The ratio of the number of blue to yellow beads used was 3 : 5. If she used 46 more red beads than blue beads, how many beads did she use in all?

Ans :- She used 200 beads in all .